K-theoretic Catalan functions

نویسندگان

چکیده

We prove that the K-k-Schur functions are part of a family inhomogenous symmetric whose top homogeneous components Catalan functions, Euler characteristics certain vector bundles on flag variety. Lam-Schilling-Shimozono identified as Schubert representatives for K-homology affine Grassmannian SLk+1. Our perspective reveals satisfy shift invariance property, and we deduce positivity their branching coefficients from result Baldwin Kumar. further show slight adjustment our formulation produces second shift-invariant basis which conjecturally has both positive rectangle factorization property. Building work Ikeda-Iwao-Maeno, conjecture this gives images Lenart-Maeno quantum Grothendieck polynomials under K-theoretic analog Peterson isomorphism.

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Dept. of Mathematics, California State University Los Angeles, Los Angeles, CA 90032, USA. Center for Combinatorics, LPMC, Nankai University, 300071 Tianjin, P.R. China. The High School Affiliated to Renmin University of China, Renmin University of China, 100080 Beijing, P.R. China. Department of Mathematics, Haifa University, 31905 Haifa, Israel. [email protected], [email protected], touf...

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ژورنال

عنوان ژورنال: Advances in Mathematics

سال: 2022

ISSN: ['1857-8365', '1857-8438']

DOI: https://doi.org/10.1016/j.aim.2022.108421